16t^2+72t+3=84

Solution for 16t^2+72t+3=84 equation:

16t^2+72t+3=84

We move all terms to the left:

16t^2+72t+3-(84)=0

We add all the numbers together, and all the variables

16t^2+72t-81=0

a = 16; b = 72; c = -81;
Δ = b2-4ac
Δ = 722-4·16·(-81)
Δ = 10368
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72\sqrt{2}}{2*16}=\frac{-72-72\sqrt{2}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72\sqrt{2}}{2*16}=\frac{-72+72\sqrt{2}}{32}
$